逆Sturm-Liouville问题的求解和解的唯一性问题

The Uniqueness and the Solution of the Inverse Sturm-Liouville Problem

通过调整核函数K(x ,t)满足的边界条件讨论一般边界条件下逆Sturm Liouville问题的求解 .同时对包括势函数 q(x)对称在内的多种情况证明了逆Sturm Liouville问题解的唯一性 .最后讨论已知势函数 q(x) +q(1 -x)所对应的一列谱如何求解逆Sturm Liouville问题 .

The problem of determining the coefficients q(x) of the Sturm-Liouville problem under the various boundary conditions using adjusting kernel function is dicussed.The uniqueness of the inverse problem in the case of symmetric potential functions is obtained.Finally the inverse problem of unique determination of the potential function in the situation when one sequence of eigenvalues is given and the potential function is of the form q(x)+q(1-x) is investigated.